Optimal. Leaf size=25 \[ -\frac {1}{6 (3 x+2) \sqrt {9 x^2+12 x+4}} \]
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Rubi [A] time = 0.00, antiderivative size = 25, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {607} \[ -\frac {1}{6 (3 x+2) \sqrt {9 x^2+12 x+4}} \]
Antiderivative was successfully verified.
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Rule 607
Rubi steps
\begin {align*} \int \frac {1}{\left (4+12 x+9 x^2\right )^{3/2}} \, dx &=-\frac {1}{6 (2+3 x) \sqrt {4+12 x+9 x^2}}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 20, normalized size = 0.80 \[ -\frac {3 x+2}{6 \left ((3 x+2)^2\right )^{3/2}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.96, size = 14, normalized size = 0.56 \[ -\frac {1}{6 \, {\left (9 \, x^{2} + 12 \, x + 4\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \mathit {sage}_{0} x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 17, normalized size = 0.68 \[ -\frac {3 x +2}{6 \left (\left (3 x +2\right )^{2}\right )^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 2.89, size = 9, normalized size = 0.36 \[ -\frac {1}{6 \, {\left (3 \, x + 2\right )}^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.17, size = 21, normalized size = 0.84 \[ -\frac {\sqrt {9\,x^2+12\,x+4}}{6\,{\left (3\,x+2\right )}^3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{\left (9 x^{2} + 12 x + 4\right )^{\frac {3}{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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